Hold firm when the work matches what they agreed and you can point at that agreement. A quality complaint with no example, or a price complaint that contradicts a signed estimate, is not a reason to cut the invoice on the spot. The firm tone says the amount stands, asks them to pay or to reply with the specific point that is still wrong, and gives a date. After that date you decide from what is written, not from a silence you have to interpret.
Settle when the gap is small beside the relationship, or when you can see you were unclear and a credit is the clean end. A $600 credit on a $4,800 invoice can be cheaper than another month of the same thread, if you would rather have $4,200 and a client than $4,800 and a fight. Write the credit down. An unwritten discount gets reopened the next time they are unhappy.
Ask for a conversation when you do not yet know which of those you are in. A call with the invoice and the estimate open is shorter than three essays. The talking tone does not give the money away and does not pretend the dispute is settled. It asks for a time by the decision date. If that date passes, you write again from a clearer place.
If the reply is still a refusal and the amount matters, the demand letter is the later document, after this one, not instead of it. It assumes you have already said what the invoice is for. Most disputes come down to what was agreed. Incusia keeps the signed estimate, the invoice and every open and reminder on one timeline, so the facts are not a memory test.